Electromotive force of a battery The definitions of electromotive force of a cell that i have read include:
1.When no current is drawn from a cell,i.e., when the cell is in open circuit, then potential difference between the terminals of the cell is its electromotive force.
2.The electromotive force of a cell is defined as the energy spent or the work done per unit charge in taking a positive charge around the complete circuit of the cell i.e., in the circuit outside the cell as well as in the electrolyte inside the cell.
MY QUESTIONS:
Firstly, I do not understand how can we measure the potential difference of the cell when no current is drawn from it, i.e., when it is in an open circuit.(according to the first definition) and even if we can measure it, i think the meanings of both definitions is not the same).
 A: We have to distinguish two meanings.


*

*Electromotive force meant as "force intensity". It is the non-electromagnetic force $\mathbf E^*$ that acts on electric current carriers, per unit charge. One example of this kind of force is that which acts on charges inside the battery due to ongoing chemical processes and keeps two poles oppositely charged at different potentials, despite strong electric field that tends to move charges to cancel this inequilibrium. Or in case of a thermal or composition gradient in a metal, the electromotive force is due to these gradients and connected natural transport of charges.

*emf "in volts". This is more practical quantity. It refers to line integral of the above electromotive intensity (force per unit charge) along some (closed or open) path in space from point $a$ to point $b$:
$$
emf = \int_{a}^{b} \mathbf E^*\cdot d\mathbf r.
$$
When no current is drawn, there is static equilibrium in battery and other nearby conductors, so the non-electromagnetic force in conductor is cancelled by electromagnetic force of equal magnitude and opposite direction. Integral of EM force intensity along the same path is
$$
\int_{a}^{b} \mathbf E\cdot d\mathbf r
$$
and since $\mathbf E^* = -\mathbf E$, this is equal to $-emf$.
Hence the rule of thumb that "emf is voltage on terminals of disconnected source". As soon as we connect the source into a closed "live" circuit, current is flowing and due to Ohmic resistance against this flow there has to be non-zero resulting force due to EM and non-EM forces everywhere in the circuit, so they do cancel each other anymore. Then $emf$ is still given by the first integral, but electric voltage by the second that can have different (lower) absolute value.
